INTRODUCTION TO "SYSTEMS APPROACH"

Gernot M. R. Winkler U.S. Naval Observatory Washington, D.C.

DEFINITION AND OVERVIEW

Systems and timekeeping have several "interfaces":

First, all systems are subject to processes, or better, processes are the essential aspect of systems. I11 all these processes, time is the one general, abstract parameter which relates the state of these processes to the state of all other systems. Time is. therefore, the universal system parameter (I).

Second, since time is the universal system interface, the use of clocks in systems is increasing, commensurate with our increasing demands for precision in systems interfacing. We now distin- guish a class of "time ardered systems" (even though in principle all systems are time ordered) in order to emphasize the precision aspects which necessitate the use of precision clocks (2).

Third, all clocks are of necessity systems; systems in which we attempt to repeat the same proc- esses as identically as possible so that we obtain a uniform time scale. Therefore, any system could be used as a clock, albeit, not a very good one, e.g. we ourselves are systems, i.e. clocks, and one can read the time off our faces!

For these reasons, since clocks are systems, and are part of systems, a general overlook and intro- duction to the systems approach has been suggested. This appears the more appropriate since some of it, the most critical aspects of the subject, fall somewliat outside the purely engineering frame of mind; the subject is indeed trans-disciplinary. Onc may even be tempted to clai~vthat these most general, but strategically essential aspects of slstems belong to philosopily in its prope sense rather than to any specific technical specialty (3).

Exhibit A attempts to sketch the scope of what is known today under various names such as cybernetics or General Systems Theory (GST). both meafiing more or less the same (4).

What is a System?

A system is a group of interacting elements or subsystems which is organized for a purpose. This purpose is clearly external or imposed in the case of artificial or synthetic systems. In natural systems, the purpose is inherent as a heuristic principle (5). The capabilities of a system are oftr. clearly reducible to those of its elements; this is the rule for technological systems of up to rathe remarkable sizes and complexities. However, very complex systems (lo8 is a most superficial di- viding mark for inter-acting elements) begin to show aspects which are qualitatively new and in principle irreducible to the qualities of the elements (6).

This is partly due to the synergistic interaction of the subsystems and partly due to principle lim- itations of our intellect. Any intellectual process as we know it is inherently an abstracting proc ess with an incredible and unaccounted amount of data compression at every one of its many stages. Even our sensory perceptions are the eventual results of a most radical selection from the flood of primitive "inputs". In the complex systems environment, however, these ignored, or be ter, unknown aspects of the systems elements inevitably come to the fore and play unexpected roles. Then we are awakened to the fact that nature is (at least for us which are its "subsystems inexhaustible (7). Such ignored parts must appear to us as an irrational part which is irreducible (see Exhibit B #5). This, then, is the origin of "emergent" qualities 8). In our aijyiication here, where we consider systems of clocks, the question will, therefore, hate to be: What are the emer- gent qualities of clock systems? We may only hint at this point that one of them is the class of advantages of having a co-ordinated system of clocks with benefits obtained for each user while contributions are made to the timing community as a whole (9).

SYSTEMS, A SUBJECT FOR THE ENGINEERING INTELLECTUAL:

A most important decision at the beginning of any system consideration is to define the level of abstraction at which the system is to be treated. One will hesitate between the "Scylla" of ele- gant oversimplification and the "Charybdis" of unmanageable complexity and confusion. One may remember, though, that as a typical scientist, one may be wont to miss the forest because of the many interesting trees and also, that the real purpose of any system approach is in fact a view and an assessment of the forest.

But, if we are to lean towards data economy, then we niust compensate this paucity with the quality of our concepts. What we wish to stress is that ingenious intuition i3 really indispensible for the discovery and the judgment of the intellectual tools to be used. i.e. the strategies. goals, concepts and hypotheses. Now inge~uityis something which can't be directed to appear on time. One has to invite it, but the humble waiting for the illuminating insight is worth almost any risk because the truly ingenious concept is literally invaluable (10).

Competent nianagement (in its usual context) is a necessary, but for systems work, not yet suf- ficient condition. As we hinted before, it is the undocumented, even subconscious experience on which much ultimate systems performance will depend (1 1). One must therefore suggest that the lack of direct, intimatc, personal bench experience of many systems engineers is in the long run very, very expensive.

The two reasons for this are: the need for an environment conducive to create thought and in- vention, and the need to train judgment and intimate experience. These should make it impera- tive to start with pilot projects, let people "fiddle around" a little, beforc serious consequential steps such as specifications writing can be taken.

One can sense at this point that a certain generosity, a largc fiame of mind, 15 a desirable systems qualification - but how could one bring anyone to a deliberate expansion of the soul? (Without inflation, of course!)

Now, in going back to the level of abstraction. we have here in these few minutes, no choice but to go for the pinnacle: Exhibit B can of necessity only be a lofty sketch, and I niay be forgiven for putting forth such conjectures as verities, alrliost as if thcy could be proved by my affirming them on oath. But. these are serious matters and thcy reprcscnt some of the basic things one finds as a resuit of great complexity.

Sonic of Euliibit B is purely metaphysical such as tf7 (which was already mentioned by Lao-tsu (12)), but some are quite plausibly related to more basic ideas: Item #6 on the list is important because "systemic" measures are disastrous. But, it is also important to understand why that must be so.

They are disastrous because they prevent the systeni trorn cvc.ltually correcting the real cause of the disturbance. The internal dynamics is being d~stortedby systcniic measures in the very direc- tion which makes thc system's state cver more precarious: it i.; the direction leading into a sudden. catastrophic system collapse (1 3). They are most interesting because the study of the effects of systemic nieasures also gives insights into the connections between GST and "infornution", correct information and not "noise". We niirst also include in the importance of information the willingness to use it. This, however, is of.en prevented by preconceived notions or "policy". The example of economic systems and their inflations is notorious (14). Such ii hypothetical system of IOU subsystems, each interacting with (let us assume) lo4 others is a system of great complexity. We may take as a coarse meas- ure thc number ot possible interactions per unit time, e.g. ,

Let us now only sketch a fcw niore points which, while they are obvious. are obviously not being acknowledged easily:

THE EXISTENTIAL LEAP IN THE DARK

Whatever we do. we are forced to act ill ignorance of the total consequences of our ac. - life is a leap in the dark. In systenis design. however. we are not totally ignorant. We ha1 !~le specifications and user experience with available rnodules as "shelf iterns" for building r

But, the crucial point is this: If we start from overall systems specifications, we will fin, ,,LZII many of these shelf items won't do the job. In order to stay within specifications we muit cus- torn design, build. test, debug. evaluate, change and produce rnany of our modules from scratch. (An item is not mature before several hundred have bcen opcrated in a systeni environment and the problems fed back to the debugging process). This. however. is a very expensive enterprise where one's resources may quickly disappear in guerrilla warfare with Murphy's Law (1 6).

The lesson is thai very successful systenis must riot come into existence via the "grand scheme" with detailed dream-specifications. One rather has to start small (pilot projectj and one should difine only general system goals (17). But, one can require that all subsystems (modules) bc items which have been in production and used sufficiently long to bring cut and correct all their hidden problems.

Such an approach does require a greater resourcefulness from your team. but you induce the ap- plication of brain power at the critical start of the project rather than for problem solving in the middle (when you hoped to be at the end). This way you don't have to lcap in conipletedarkness.

Another point is more subtle so let us invokc an appropriately exotic cxample:

THE SIAMESE CAT

Let us consider the procurement of such a "systeni". Unfortunately. we cannot order it ar?ymore as it used to be done: "One cat (Siamese) each . . . 550.00". Now, we need specificatioiis and they niust be complete or exhaustive - but can they be complete?

As we learn from biology. a cat's bpecifications are embodied in its genes. s total of about 1010 bits of information. Prof. Carl Sagan has actually proposed (18) that we should scnd these 101° bits of information by radio to an alien civilization. This would then enable them to get cats just like ours here on Earth. Now to be charilable, we assume such proposals to be in jest be- cause they would reveal a cor~ipleteignorance of rather vital points in systcnrs engineering and specifications! There would simply be no cat on the basis of these IuIO bits unless wc could aisu enable that alien civilization to reproduce exactly the totality of our terrestrial e~.lvironmcntin which we mass-produce our cats. (In that case, unlikely as it is, they would a!so have to select a competent and honest contractor. a hard task. because the also in1po;tcd rules. as part of the en- vironment, may hinder that!) We, therefore, conclude that we need much mote than the 101° bits - but how much?

Just the network of the cat's 1O1O neurons has up to about 40 interconnections (synapses) per neuron. A description of it would require an amount of information vastly in excess of our 10'0 bits in the genes. We get a glimpse of the tantasttc magnitude of this information problem but we still could not assemble the system unless we have all the information, or could we (19)? The Siamese cat has helped to shed light on the question of how nature builds such extremely coni- plex and well functioning systems on the basis of clearly insufficient information (20).

It 'urns out th~tone of the characteristics of the Siamese cat, the grey color of its fur, is caused by a simple gene mutation. This mutated gene cannot, as the normal gene docs, produce the pig- ment melanine at 37OC. Now strangely this failure also causes a second peculiarity which is not obviously related to it: The cross-eyed look and the specific behavior of this cat. The reason for this is that i:iey also have some of their "wires" crossed, i.e. parts of the optical nfxrvesend up in the wrong cerebral hemisphere (21). This produces the need for compensation with some further changes in brain structure during growth. It a!so induces different behavior. that is why they look a little cross-eyed.

But, how can the failure to synthesize melanine also cause such considerable char;.cs in the growth and structure of the nervous system? The revealing answer is that the absence of melanicie in the early stdges of cell division crea'es a different enviidnment for cell specidlization whicl~now Sol- lows different paths. What the growing organism does is that the chemistry code only modulates the environment, but the actual task ot' speclfic design is execut2d bv the generations of dividing and specializing cells, the specific specialization Leitlg induced by the local environment which in turn is being changed by the collective effect of the dividing (and specializing) cclls.

That is what is called organic growth - the systcm is self designing. One can learn from nature beczuse a living system such as the one discussed is tlie result of billions of selections and modi- fications. If we want to apply principles which correspond to organic growth. thcn we nlust also include substantidl redundancy, a large reserve capacity (a large margin of performance) and suf- ficient feedback and internal control at the lowcst possible level. Large coniplex systems have features which in some ways rescmble an organism except that we cannot afford to usc nat~~rc's wasteful techniques of evolution. Instead, we have to use reason and foresigl~t. We are not yrt doing too well in that department because we must remember that the pu5lic disenchantment with technology has a simple cause. It is not a consequence of too niucii thinking on our part. It is often intellectual arrogance which prevents completely thorough inti*llcl-tt~alpreparations. It is also often a tolerance cf sloppy, superficial thinking. Therefore, a : ' 3cientific attitude. most helpful in the face of large problems, is not pride and conceit, but we adn~issionof igno- rance and eagerness to learn.

As a summary, one may look at Exhibit C. LC-;leof truth ncans also hate for the half-trdth 111d the nicaningless. Humility, preached since Socrates, is often eclipsed by the mistaken desire to project an appropriate image. Patience, finally, is rarely appreciated by cagcr beavers who helicvc in frequent transplanting as a stirnulus to growth. But. this is not so. To build a competent team requirrs a couplc of years. Any tech1 i.31 management which redirects arid it!organlzc> every year, simply does not know what to d~.It is. after all, not piniriiicks wliicli r;i,~ke.! Idrpe systcm a success, but creative, thorough thinking and a very sustained effort necessary to rcducc it to practice. EXHIBIT A

MAIN ASPECTS OF SYSTEMS THEORY (GST - CYBERNETICS)

1. Linear Systems: Feedback, optimal control, stability - systems synthesis from known ele- ment paramsters. Systems architecture (22). 2. Proczss Statistics: Estimation theory, filtering and prediction - pattern recognition (23). 3. System Measure~nentsand System Identification: How to characterize system performance abstractly. Links to epistenlology (24). Physical causes vs. teleological causes (goals).

4. Information Th 3:I. Storage (memory), processing - semantics (meaninp' - artificial inte ligence - strategies. (Theory of games) (25). 5. Advanced Mathematical Tools: Infinite dimensional state spaces, nonlinear systems, adaptiv systems; systems modelling and simulation; catastrophe theory. Fuzzy sets, recursive an computable sets.

6. Self Organizing Systems: Emerging properties, synergy.

7. Systems, Their Environment and MAN; the Questions of Policy: Man - system interfaces, "Operations Research" (26).

8. System Reliability: Self repairing and redundad systems. System Life cycles and support (27). EXHIBIT B

SOME GENERAL SYSTEMS PRINCIPLES

1. If anything can go wrong, it will (follows from complexity which assures that eventually the ever present disturbances will test every weakness). Also, known as Murphy's Law.

2. Le Chatelier's Principle: Systems tend to oppose attempts to change them. (In order to function, however poorly, a system must be in internal dynamic equilibrium in its element interactions; therefore, a new input will immediately bring forth compensating forces) (28).

2a. Corollary: If a system should ever work well, then don't touch it!

3. Systems grow (at least due to the after thoughts) (29).

4. A complex and working system can only evolve from a simple and working system (evolu- tionary growth).

5. Every very complex system contains irrational features; they are necessary for functioning.

6. Symptomatic cures are uszless, they only make things worse. The same is true of "systemic" cures (system-wide, sweeping measures, see principle #2). People who don't understand sys- tems love systemic cures!

7. An overdose of the best measures (beliefs, principles. ideas. etc.) is poisonous. (Also, known as the DIALECTICAL (30) Principle in some ideologies - namely in those who overdo this principle also!)

7a. Corollary: You can't be perfect; any attempt to be, or to make a system perfect will have disastrous consequences. (That should not mean that one must stop at the level of mediocrity!)

8. The behavior of complex systems becomes unpredictable as the conlplexity increases. (See also principle #5)

8a. Corollary: Extremely complex systems are beyond human capacity to evaluate.

9. A system (composed of subsystems) which can operate well with little internal control and data flow will also be highly resistant to failures and external disturbanca. Examples; An atomic clock with excellent crystal oscillator; A time ordered system with largely ir~dependent clocks; An organization with properly delegated authorities; A society with citizens of corn- mon high moral standards.

10. The main cause of system instabilities are the delays in the action of the subsystems on each other. Very large and complex systems, therefore, have no defined equilibrium state (static) and are, therefore, subject to corresponding process statistics (such as flicker noise. random walk, Pareto distribution. etc.) (31). (See also principle #8)

11. Engineering of systems is a hard compromise between opposing desirable features. Systems optimization must include all aspects and is usually successful 3nly if some flexibility of specifications is allowed (33). EXHIBIT B (Continued)

1. Any theoretical treatment of a system has an optimum degree of complexity (such as num- bers of parameters. etc.). The optimum corresponds to a "best" separation of essential from accidental features (or of determitiistic from random effects) and it is usually better to err on the simpler side (32). EXHIBIT C

THE CARDINAL SYSTEMS VIRTUES

TRUTH - Keep The Coefficient Of Fiction Small.

HUMILITY - We Know Very Little. Keep Learning.

PATIENCE - Good Things Need Time. NOTES AND REFERENCES

(I) Time as an abstract parameter for the comparison of different processes is discussed and re- viewed in

Marton, L. (ed) (1977) "Advances in Electronics and Electron Physics" Chapter 2. p. 34-45, ACADEMIC PRESS, dew York ISBN 0-12-014644-4.

(2) "Time Ordered Systems " Time and Frequency, FTTI Systems - all refer in a general way to the enhanctd importanc: of precise time or frequency in these systems. However, one has to be specific in terminology and should distinguish between (a) equal frequency, (b) accu- rate (a priori, without calibration) frequency, (c) internal synchronizatic,i without account- ing of differerctial prop?garion delay and/or frame ambiguity resolution, (d) internal synchron- ization with ambi~uityresolution and/or delay acco,nting and (e) systems which are synchron- ized or caordinated (i.e. whether the time constant is short or very long) with UTC. The step fr~mIC; to (d) is expensive. from (d) to (e) is not, yet it brings the typical full syner-

gistic kncfits of being a member of a user community. An exampie fc;i (a:) is the TV. while ne wcrl.. syncionization needs usually (d). See the following for a valid recommendation to take, in this case. the easy additional step (e).

Stover, H. A. (1973) A Time Reference Distribution Concept for a Time Division Communi- cations Network. Proceedings 5th PTTI Conference p. 505-523.

(3) The converse seems also to be trke as the followiilg may suggest: We only have to substitute systems for the word "being" (Monas, povasj and we can immediately understand in our terms the great Renaissance thinker Giordano Bruno when he postulates the universe as a hierarchy of "beings". Now Monas means something which is simple, a unity; a concept which originated from the introspective experiences of one's soul. But. this unity and sep- arateness is deceptive and also makes his view somewhat inconsistent. The soul is due to the synthesis of the sensitivities of the body which are rooted in the (admittedly mysterious) properties of matter and these are universal and eternal (Spinoza: "Sentimus experim~rque nos aeternos esse"). Therefore, there is nothing separate about the soul except the limited memory. Conversely, we may see a system as a Monas (black box) because the system con- cept is purely heuristic, is an intellectual device to divide the world into interesting and man- ageable parts with the dividing "surfaces" somewhat arbitrary (and the system "transfer func- tion" could be called its character); in other words, the world is a hierarchy of subsystems. Now some of these subsystems have fates which can be almost independent of the rest of the universe for long times. Stable atoms and particles are such (closed) systems and we attempt to use them as clocks. However, completely closed systems can't be predicted from the outside and we can see here clearly the connections to "causality," "indeterminism" (or freedom) and similar general questions.

(4) The literature on GST as well as on the areas of Exhibit A is now enormous. A few general items follow:

Bertalanffy, Ludwig von (1968) "General Systems Theory." Brazillcr, N.Y. Also published by Penguin University Books, 1973.

Bertalanffy, L. and Rappaport, A. (ed) (1962) "General Systems" Ann Arbor General Sys- tems Research.

Fox, V. (ed) (1965) "System Theory," Interscienc~Publication, Polytechnic Press, Brook:yn, N.Y. (Lib CCC#65-28522). Klir, G. V. (ed) (1972) "Trends in GST," N.Y. (Lib CCC#7 1-178 143) John Wiley.

Gall, John (1975) "Systemantics." QuadrangleIThe New York Times Book Company (an amusing, but a little to-be-taken-seriously farce).

Guillemin, Ernst ( 1963) "Theory of Linear Physical Systems," J. Wiley .

Forrester. Jay W. (1961) "Industrial Dynamics" and

Forrester, Jay W. (1971) "World Dynamics," Cambridge, Mass. (Lib CCC#7O-157752). (These last two deal with systems dynamics and model building at a large scale.)

(5) By that we mean the teleological explanations. But teleology is purely a heuristic device in science; in philosophy it may be more, much Inore, because such teleology can only be grounded in some metaphysics.

(6) There is no simple measure for complexity or size of the systems because such measures would have to reflect not only the number of possible interactions per unit of time, but also take into account the complexity (or the character) of the interacting subsystems. Obviously an organization of 100 people is vastly more complex than a computer with lo8 transistors - but only if they interact.

(7) For a discussion of "inexhaustibility" under the quantum - mechanical point of view see the concept of "qualitative infinity of nature" in

Bohm, D. (1957) "Causality and Chance in Modern Physics." Viin Nostrand.

In our context, however. we offer sirnply the conjecture: There are only subsystems, no real elements.

(8) Emergence is an important concept in British newer metaphysics:

Alexander. Samuel (1977) "Space, Time and Deity." Dover. N.Y.

Here, however, it is based on the informational aspects of epistemology and is much closer to p. 61-81 of

Broad. C. D. (1925) "The MIND and its Place in Nature." Kegan Paul, Trench, Trubner and Company. Ltd. London.

(9) This aspect is discussed in reference (1) p. 79. But, the paper by S. Stein and F. Walls which followed this presentation gives yet another aspect of an emergent quality, i.e. better per- forniance obtainable from a combination of two different oscillators. This IS a most impor- tant subject for this conference.

(10) Here again it is hard to ovcrempllasize to an audience sa rooted in the real and material world as one is today. the fact that some insight gained by concentrated thought is the basis of everything we do today in R & D. And, conversely, everything will become obsolete through another idea. Even more, one could support yet another conjecture: The larger thc task. the more sensitive it is to thc effects of creative thought.

(I 1) This is even true for our laws, for anything docurnentcd. Polanyi has pointed out that any system of rules can only be transmitted by tradition. exar~lpleand training. This is clearly a precarious process and the inforn~ationso transmitted is wide open to profound changes al- beit froni one generation of practitioners to the next. Now it is the bureaucratic ideal to leave nothing to discretion, but to embody everything in rules. But, any rule must be inter- preted in a concrete case and this would require another rule. However, let us assume that -311 existing rules were united into a single code; then this code, obviously, could not contain prescriptions for its own interpretation, i.e., our ideal has a principal flaw. We do eventually depend upon responsible, creative interpretation. See

Polanyi, Michael (1946) "Science, Faith and Society," p. 58. University of Chicago Press. (ISBN 0-226-67290-5)

Now if the abovc is true for a body of laws and regulations, then it is a fortiori true for technoiogy where so much depends on the skills, the tricks and trained judgment 9f the prac- titioner. In fact, a trade, even a rechnology, gets irretrievably lost if not practiced. That means that the great majority of know-how developed every year in our national R & D efforts is completely wasted because of the haphazard way in which support of such group: becomes allocated. It would be wise to implement more long range funding plans of R & D teams by mission oriented agencies, such as the DoD. under this aspect.

(1 2) Lao-tsu (-500 BC) "Tao-te-ching," Vintage Books 1973, ISBN 0-394-7 1833-X.

This is an antidote to the instinctive managerial chrestomania. Ldo-tsu was the first to teach that one sees more by not focusing on a single point; that one accomplishes more by not running blindly after a single goal. Today these basic idezs of Taoism find their corrobora- tion in the organic view and in the concept of organism.

We can consider principle #7 of Exhibit B to be of principal importance for any intellectual treatment, of large technical systems as well as of our social situation at large in which, after all, 211 our technical systems are embedded. Since our social structure as well as our personal attitudc rests on a fundamentally inconsistent system of tacitly assumed values and principles, we try to cope by falling from one extreme application of a certain A to an equally extreme one of another "good" B, after the results of the previous excess become painfully obvious. It is for this reason that successful, i.e. long term beneficial systems engineering can be done well by people who have gained that inner directed, self-disciplined attitude which helps them to abstain (out of wisdom, not interest in near term) from overdoing the "best," i.e. from maximizing the "profits." Hence, the claim about the necessary expansion of the soul; and hence, the problems created for science and engineering by the weakening of the liberal arts in education in the course of the post-Sputnik hysteria. One can safely claim that a clear awareness of the need for balance is the prerequisite for any use of intellectual tools. After all, those are more effective and potentially more disastrous than atomic bombs (which are only their by-product).

(13) That is a subject of great recent interest and has become known as "Catastrophe Theory." See e.g.

Zeeman, E. C. (1976) "Catastrophe Theory" in Scientific American. p. 65 (April).

(14) Another notorious and often tragic example is the complex of unintended effects if a specific management problem such as incompetence in some places is being attacked with general re- organizations. Such measures are of course sometimes needed such as when the organizational input-output is to change. But, as synlptomatic cures they are disastrous because as systemic cures they disrupt internal communications. See particularly Lawrence, Paul R. (1955) "How to deal with Resistance to Change" in Harvard Business Re- view: "On Management," Ch. 22, Harper & Row, ISBNO-06-011769-9 and

Drucker, Peter F. (1973) "Management," Ch. 48, Harper & Row, ISBN 0-06-01 1092-9

Organizations are also systems, but even more important, any system effort is of necessity a team effort and the first question always to be asked is: How can we get a competent team organized and motivated'? Money is only a necessary, but not sufficient resource.

(1 5) A large scale system has been defined as a system "whose large dimensionality makes the ap- plication of standard analysis techniques infeasible due to excessive computational require- ments." A discussion on stability and optimization of such systems can be found in

Mageiron, E. F. (1976) "Topics in the Study of Inter-Connected Systems." Technical Re- port 664, Div. Trig. and Appl. Phys. Harvard.

On the other hand, a system has also been defined as large "when decentralized control can provide acceptable performance." See

Suri, Rajan (1978) "Resource Management in Large Systems." Technical Report #67 1, Div. Appl. Sc. Harvard University, p. 185.

We propose to call a system large when it can only be dealt with by statistical measures; and very large when entirely new, irreducible features emerge. By thiq definition. the U.S. econ- omy is a large, but not yet a very large system (since it can go broke through foolishness, just like a family can).

(16) Once a system is in operation, it is too late to improve poor reliability. Tile larger the sys- tem, the more critical will be error free operation. Now transient errors in computers. e.g.. are several orders of magnitude more frequent than actual hwd failures. The best way to check for transients is hardware redundancy built into critical points. In our application of time keeping, the soft failures are large clock rate changes and here the only way to filter them is clock redundancy. In general, hardware redundancy gives the capability of continu- ous systems diagnosis, i.e. the decoupling of reliability from other problems. Set. also

Percival, D. B. et a].. (1975) "Time Keeping and the Feliability Problem." Proc. Ann. Fre- quency Control Syni;:osium, Atlantic City, N.J. 29/41 2-41 6.

(17) The "start small" recommendation has as an alternative the advice to proce:d if possible only with dividable efforts. Such efforts are those where any intermediate stages are fully beneficial. Bui1dir.g a system of new, high capacity trunk lines is a dividable effort. If money runs out, the effort t~xpendedwas not wasted. The GPS program (certainly for time dissemination) is also largely in this class. Benefits do not have to wait until everything is perfect. In contrast, a tunnel is clearly not a dividable effort: neither is a bridge.

(18) Sagan, Carl (1973) "Communication with lixtratcrrcstrial Intelligence." MIT Press, Cam- bridge, Mass.

(19) If we accept the thesis of incxhaustil~ilityof nature (7).then it is clear that no inforn~ation will suffice to reproducc a natural system exactly. The casc is entirely different for artificial systems because they represent the result of abstract functions as conceived by an intellectual process of finite steps. In this casc, the ignored aspccts of the material implementation play only a tolerably disturbing rolc - until we cxccetl a certain complexity. (20) While no finite amount of discreet (abstract bits) information may suffice to duplicate exactly our cat (which would have to include its acquired behavior). we can quantify the informa- tion which is sufficient to launch the germ cell on its development. i.e. the modification and acquisition of parts of its e~vironment.The information is quantifiable and "simple" (10l0) because it is relative to the triaterial in the cell and its environment. This is where we have still hidden the inexhaustibility.

(21) Guillery, R. W. (1974) "Visual Pathways in Albinos." p. 44-54, Scientific ,\merican. May (See also lit. cited at p. 144 and Nature 252, 195-199, 1974).

(22) The practicality of digital control loops has opened up a new horizon even for simple straight- forward systems such as a quartz clock which i. locked to an intermittently available refer- ence. One is not limited anymore to the t:lpc 1 vs, type 2 (or 3?) loop question, but can now consider much more sophisticated control, i.e.. along the lines discussed in reference (23d). As general background refer to chapter 17 of (77). Of particular interest to tirne and frequency users is also

Gardner. Floyd M. (1966) "Phaselock Techniques." John Wiley LCCClf66-22837.

An excell; nt introuuction to the advanced mathematics of extrcmal problems with con- straints is

Gumowski, 1. and Mira, C. (1968) "Optirnization in Control Theory and Prscticc." Cam- bridge University Prcss ISBN 511-05 1 58-4.

(23) a. Koopmans, L. 11. (1974) "The Spectral Analysis of Time Series," Academic Press, N.Y. ISBN 0-1 2-41 9250-5.

b. Box, G. E. P. and Jenkins, G. M. (1970) "Time Series Analysis, Forecasting and Control," Holden-Day, San Francisco. LC'CC#77-79534.

c. Morrison, N. (1969) "Introduction to Sequential Smoothing and Prediction." McGraw- Hill. N.Y. LCCC#69-17187.

d. Percival. D. (1978) "The U.S. Naval Observatory Clock Time Scales," Trans. IEtlE-IM Dec.

The first two treat randoni variables after systeniatic parts ha\. been removed. Morrison deals with estimation of deterministic functions in the presence of additive randoni ertors. Percival discusses the application of ARIMA models (the Box-Jenkins approach) to the ireat- rnent of clock sets.

(24) For the treatment of vzry complex systems. it i., ncccssary to be quite clear about what we mean by "cause." "model," "law," "probabilistic explanation," etc. These are concerns of practical relevance, e.g. why do we have confidence in extrapolations with deductive nomo- logical explanations - causal laws, when we should be very suspicious of extrapolations with a purely tnathematical model? For the pure empiricist, the difference is harder to justify than for the rationalist (or for a mitdieval realist, or Platonist). It is no accident that the treatment of the most basic systems in science, i.e. atomic and particle physics and of the most complex, possibly inexhaustibly complex. s: .ems, i.e.. in biology. h:~sbrought about an unprecedented concern of those scientists with epistemology. As a very first starter, the fol- lowing is suggested: Reynolds, P. D. (1971) "A Prinler ir; Theory Constructior.," Bobbs - Merrill, Indianapolis ISBN 0-672-61 196-1.

(25) We can recommend a reference which is of interest beyond the scope of its title because it gives very instructive examples for difficulties of quantification and discussions of "utility," "rational behavior," etc. It is a classic:

Neumann. John von and Morgenstern. Oskar (1944) "Theory of Games and Econo~nicBe- havior," John Wiley and Sons, Inc., N.Y. ISBN 04719 1 1857.

(26) Wagner, Harvey M. (1975) "Principles of Operations Research" Second Edition, Prcntice Hall. Inc. ISBNO-13-709592-9 is a textbook with many "mind expanding" exercises! To work through these 1000 pages (this author has not!) should give a firm grounding in OR.

(27) An excellent general overview is given in

Giacoletto, L. J. (cd) (1 977) "Electronic Designers Handbook," Section 28 (by Trent). McGraw-Hill. ISBNO-07-023 149-4. (See also note ( 15))

(28) A logical corollar~.to principle $2 of Exhibit B would be: Indirect approaches often work better (because they avoid the system reaction. at least it is delayed into ineffectiveness). The best treatment. of course. would be a thorough understanding of the causality of the sys- tem dynamics. but this will be available only in systems of modest complexity. (See also principles #5 and #6 of Exhibit B.)

(29) Since these after-thoughts seem to be inevitable, it will be wise to make provisions for them, i.c. to allow for expansion in the basic architecture.

(30) Unfortunately, I-legel, the inventor of the modern sense of "dialectic." confused an epistem- ological with an ontological issue. In explaining things, the isolation of opposing ideas is an important intellcctilal device. In :he ensuing discussions, the extremes find a synthesis which is a better explanation than eithcr of its components. the thesis and antithesis. But. this purely explanatory aspect has nothing to do with a common S property - the tendency to invert things. Examples are in the bible (1 Cor. 1.27): Plato (Laws 4, 705); Aristotle calls it "Reversal of roles" ("pcripeteia" in Poctica VI. 18); and Toynbcc in his "A Study of f-listory" (Oxford University Press 1973, ISBN 0-5 17-1 7941 5)in Clis. 22 and 33 gives historical ex- amples whcre failure was caused by early success.

In modern terms. Russell (Authority and tile Individual, Simon and Echuster, N.Y. 1949, p.

9 and 66) suggests that Security is :I lisguided goal in social perfection. In the most ab- stract terms, one can state it as follc.,,?;: An i~nbalsnced.single minded application of an A will be inverted through thc S process into its eventual oppcsitc. with thc effect as if A-I would have !)ten applied.

Examples: A large system designed with sole enipllasis on cost will, through breakdowns and deficicncics become more expensivc than a reasonably generous design. A timing system de- signed with ~naxinlumemphasis on pcrforniance margins will, through the use of "racing liorsc" type clocks. bccor~icvery touchy, personnel dependent and generally unreliable.

(A burcaucratic system dcsigncd for centralized efficiency with tight control and detailed procedures will bccomc unresponsive to needs, extremely wastcful anti an easy target for tht. nlost blatant corruption (see also (I 1 ).) Now the tragic confusion, mentioned above, was inherited by Hegel's materialist successors who always see in such instances "contradictions" instead of real system reactions. Contra- dictions are a purely logical affair - we create them if we are confused and inconsistent. And. a synthesis may come in discussions, but the system will not find it - they will oscillate wildly. Contradictions are only in our theories, never in the phenomena. Those will go their way, whether we see "contradictions" or not.

(31) Mandelbrot, B. (1963) "New Methods in Statistical Econoniics," J. of Political Economy 71. 421 makes the point that large systems often exhibit statistics with sorile internal correlations ("Flicker noise" in clocks, "random walk" and "Pareto" distributions in economic systems). Such systems are hard to investigate because in the presence of such behavior, a basic deter- ministic perforrnancc cannot be discerned, i.e. perceived structures may be due to chance. We claim that this must be expected in highly complex systems with delays (which may be integration effects such as, e.g. crctiit expansion takes a long time until its inflationary et'fects become noticeable).

(32) This is variously known as Occam's Razor (do not use more concepts than necessary); Mach's principle of econoriiy of thought (the simplest theory is the best); the principle of parsimony: etc. In primitive terms, it means that one should use the simplest niathematical model for smoothing because otherwise one accepts random components as part of the deterministic model which is disastrous tor any extrapolation! See also the interesting numerical example of finding the degree of a noise - contaminated unknown polynomial in

Scheid, F. (1968) "Numerical Analysis," Ch. 21. p. 250. Schaum's Outline Series, McGraw- Hill. N.Y.

(33) System Optimization (principle #I 1) has also aspects which must be considered under the "Reversal" principle (#7). The "Tragedy of the Commons" syndrome (see Hardin in Science 162/p.1243, 1968) can be generalized in so far ns optinlizztion of the subsystems without regard to the system leads to poor performance if thifigs work at all. This is so because "the whole is more than the sum of its parts".